1. Field of the Invention
This invention relates to liquid crystal devices and more specifically to drive waveforms for switching dual-frequency liquid crystal (DLFC) devices at large tilt angles.
2. Description of the Related Art
Liquid crystal devices have many different electro-optical applications including tunable waveplates, spatial light modulators, displays, color filters, gratings, beam steering devices, optical switches, etc. . . . Application of a voltage across a liquid crystal cell modifies the polar angle or ‘tilt’ of the liquid crystal molecules on average, which in turn changes the birefringence of the cell. The birefringence can be used to change the polarization and/or phase of an incident polarized light beam without affecting beam intensity. Modulation of the liquid crystal devices can be either binary (on/off) or gray-scale (continuous or discrete) and can be done pixel-by-pixel, for groups of pixels or for the entire LC device.
In liquid crystals the electro-optic effect results from the anisotropic nature of their molecular structure 10. The physical properties along the LC director 12 (average molecular axis) differ from those that are perpendicular to the director. In particular, the dielectric anisotropy Δ∈=∈∥−∈⊥ allows the director to be oriented either parallel (Δ∈>0) or perpendicular (Δ∈<0) to the applied electric field as shown in FIG. 1. The refractive index of LCs is also anisotropic. Thus the rotation of the LC director under the influence of an electric field changes the effective refractive index of the LC medium which alters the polarization state of the light passing through.
As simple yet important components in optical systems, liquid crystal tunable waveplates (LCTW) are used to adjust the phase delay of one of the polarization components of an optical beam, resulting in desired changes in the polarization status of the beam. An example is given in FIG. 2, where a linearly polarized incident beam 20 having a linear polarization 22 is passed through a LCTW 24 with its optical axis 26 aligned at an azimuth angle of 45° (direction of phase retardation) with respect to the incoming polarization to output a beam 28 with a 90° polarization rotation 30. The rotation happens only if the LCTW is turned to be half wave plate for the given wavelength. A 0° polarization rotation happens only if the LCTW is tuned to be full wave plate for the given wavelength. The tilt of the liquid crystals is controlled to produce the necessary change in average effective birefringence Δneff for the half and full wave plates, respectively. And the induced retardation in the wave plates is dΔneff, where d is the LC cell thickness. This ‘core’ LCTW can be used in many different applications depending on, for example, input components to polarize the input beam, modulation of the LCTW and output components to readout the polarization or phase delay written onto the carrier beam. These configurations and techniques are well known in the art.
In liquid crystals the induced change in the average effective birefringence or retardation is approximately linearly proportional to the applied holding voltage from roughly 10-45 degrees of tilt. To achieve tilt angles greater than about 45 degrees, the voltage becomes highly nonlinear and much larger, and the maximum tilt is about 85 degrees. The average effective birefringence is also a function of cell thickness, the thicker the cell the more birefringence changes for a given tilt. For current narrowband applications, the cell thickness is selected so that a range of tilt angles in the LC's linear range produces a desired range of birefringence. For example, LCTW 26 can be configured so that it can switch between a low tilt angle in the linear region that produces an effective birefringence for a half wave plate that rotates the polarization by 90° at the given wavelength and a high tilt angle in the linear region that produces an effective birefringence for a full wave plate that does not affect the polarization of the light at the given wavelength.
In most applications, it is desirable to switch the liquid crystal cells from the low field state to the high field state and vice-versa as fast as possible. The average tilt of LC molecules within a cell is set by the amplitude of the voltage across the cell, the larger the voltage the greater the tilt. In theory the DC voltage across the cell can be changed to modify the tilt to achieve a desired effective birefringence. For reasons having to do with lifetime issues, a low frequency AC voltage is applied with the peak-to-peak voltage determining the tilt. When switching low to high, the AC voltage is increased and the molecules respond to the electric field by pushing towards the higher tilt state against their ‘elasticity’. The steady-state ‘tilt’ is where the electric field push balances the elastic pull. It is well known that the switching speed can be increased by first applying a larger ‘kick’ AC voltage to switch the molecules and then reducing the voltage to a steady-state hold value. When switching high to low, application of a much smaller ‘kick’ voltage unfortunately does not cause the molecules to respond to the electric field by being pulled down to their low tilt state. Application of a smaller amplitude voltage merely reduces the push. Consequently, 0 V is suitably applied to the LC to remove the electric field, hence ‘push’ thereby allowing the molecules to relax back to a desired tilt set by a lower steady-stage hold value. Relaxation is a slow process, the 0 V signal may be applied for as long 10 ms before the low tilt state is reached and the holding voltage can be applied. As a result, liquid crystals in the visible and near-IR bands switch low-to-high in less than 1 ms typically but switch high-to-low in typically about 10 ms, which is not desirable.
In the early 1980s it was discovered that for certain ‘dual-frequency’ liquid crystal materials if the frequency of the drive waveform were increased beyond a crossover frequency the molecules would exhibit an inversion of the sign of the dielectric anisotropy and thus would react to the same electric field when switching high-to-low by being pulled back to zero. Thus the molecules could be actively driven in both directions by changing the frequency of the high-amplitude kick waveform thereby reducing the switching times to about 1 ms in both directions. A typical electro-optical response 40 of a DFLCTW switching between λ and 4λ(λ=632 nm) and the dual-frequency drive waveform 42 for switching low-to-high and high-to-low is illustrated in FIGS. 3a and 3b. Here λ represents a retardation that is equivalent to a full wave of λ. At 90 degree tilt, the retardation is 0. At some lower tilt angle, the retardation is λ and at an even lower tilt angle the retardation is 4λ. In this example, the crossover frequency is approximately 25 KHz. As shown in FIG. 3a, the drive waveform includes a low amplitude low frequency holding voltage 44 of 3.3V@4 Khz to hold the LC in a low tilt state. To switch the LC to a high tilt state, the drive waveform is switched to a high amplitude low frequency kick voltage 46 of 40.6V@4 KHz that pushes the molecules against their elastic forces to a higher tilt state. Once switched, the voltage is reduced to a high amplitude low frequency holding voltage 48 of 7V@4 KHz where the ‘push’ and ‘pull’ forces are in equilibrium. As shown in FIG. 3b, to switch high-to-low, a high amplitude high frequency kick voltage 50 of 37.5V@50 KHz is applied creating a large electric field that ‘pulls’ the liquid crystal molecules back to the low state. The LC can switch in either direction in about 1 ms.
Andrew Kirby and Gordon Love in their paper entitled “Fast, large and controllable phase modulation using dual frequency liquid crystals” 5 Apr. 2004 Vol. 12, No. 7 OPTICS EXPRESS pp. 1470-1475, noted that dual frequency control has not widely been used due mainly to the complexity of the control method. The enumerated three complications: “There is not a simple relationship between the starting phase, the next desired phase and the required voltage sequence”, “The LC must not be used near to saturation, otherwise the plane of the director can become undefined and scattering occurs”, and “High frequency high amplitude voltages must be applied with care, otherwise damage due to heating in the LC cell can occur” thus reaffirming the accepted practice of configuring dual frequency liquid crystals to operate in the linear region. Kirby and Love reported on a method for high speed, large stroke phase modulation using dual frequency control of liquid crystals.